1 00:00:00,580 --> 00:00:08,350 Let's do this question, Esquire style of length, 20 centimeter as four quarter circles at each corner 2 00:00:08,470 --> 00:00:09,890 as shown in the figure. 3 00:00:10,330 --> 00:00:12,650 Find the area of the shaded portion. 4 00:00:13,000 --> 00:00:14,620 Now, that's the spot over here. 5 00:00:14,680 --> 00:00:15,090 All right. 6 00:00:15,280 --> 00:00:19,420 Another tile with the same dimensions has a circle in the center of the tile. 7 00:00:19,670 --> 00:00:20,550 This is the second one. 8 00:00:20,560 --> 00:00:20,910 All right. 9 00:00:20,970 --> 00:00:21,700 Is the first one. 10 00:00:21,940 --> 00:00:22,870 Is the second one. 11 00:00:23,410 --> 00:00:29,320 Now, if the circle touches all the four sides of the square to find the area of the shaded portion, 12 00:00:29,320 --> 00:00:34,970 which is this part way here in which tile area of the shaded portion will be more. 13 00:00:35,110 --> 00:00:37,240 Remember, we have already discussed this. 14 00:00:37,270 --> 00:00:38,590 It will be the same, right. 15 00:00:38,770 --> 00:00:43,370 If you join this and this together, you will see that this part over here. 16 00:00:43,690 --> 00:00:45,430 And if I join it over here also. 17 00:00:46,590 --> 00:00:52,410 You will see we have discussed that this and this are equal right now, let's see it again so that you 18 00:00:52,410 --> 00:00:53,760 solidify your understanding. 19 00:00:53,940 --> 00:00:55,800 Now, I'm already telling you the answer. 20 00:00:55,920 --> 00:00:59,700 You should be able to do this question in five seconds because we have already discussed it. 21 00:01:00,030 --> 00:01:01,250 But let's again discuss it. 22 00:01:01,730 --> 00:01:03,560 This case one is this case two. 23 00:01:03,820 --> 00:01:04,290 All right. 24 00:01:04,440 --> 00:01:08,310 Now, the area of the trial is 20 to 20 because it's a square, right. 25 00:01:08,520 --> 00:01:10,690 That's equal to 400 centimetre square. 26 00:01:11,010 --> 00:01:11,490 All right. 27 00:01:11,640 --> 00:01:14,060 Now, over here, this is the radius, right? 28 00:01:14,190 --> 00:01:19,590 So let me marketers are so this is also equal to our two hour is equal to 20. 29 00:01:19,740 --> 00:01:22,560 Therefore, are is equal to 10 centimetre. 30 00:01:22,650 --> 00:01:23,010 Right. 31 00:01:23,760 --> 00:01:24,200 All right. 32 00:01:24,330 --> 00:01:25,820 So what would be this area? 33 00:01:26,070 --> 00:01:29,730 This area will be won by sort of by our square. 34 00:01:29,740 --> 00:01:32,210 Right, because this is a quarter of a circle. 35 00:01:32,340 --> 00:01:36,010 So one by four off by our square where all is equal to 10. 36 00:01:36,300 --> 00:01:40,650 Now, if you want all these four together, you need to multiply this with four. 37 00:01:40,770 --> 00:01:45,120 That's four in the one by four into Pyar Square, which is the same as by our square. 38 00:01:45,150 --> 00:01:45,510 Right. 39 00:01:45,750 --> 00:01:46,230 All right. 40 00:01:47,200 --> 00:01:53,620 Now that that would be three point one four into 10 square, which is approximately three hundred and 41 00:01:53,620 --> 00:01:56,530 fourteen centimeter square, so what's the answer? 42 00:01:56,800 --> 00:02:00,120 The shaded region will be four hundred minus three, one four. 43 00:02:00,280 --> 00:02:05,140 And remember, it's this part that was shaded in the question that's 400 minus three hundred and fourteen, 44 00:02:05,350 --> 00:02:08,260 which is approximately eight to six centimeters square. 45 00:02:08,410 --> 00:02:13,560 Now I tell approximately because three point one four is the approximate value of PI. 46 00:02:13,840 --> 00:02:14,290 All right. 47 00:02:14,470 --> 00:02:21,820 Now, let's see the second case over here, the diameter is two are and two are again, is equal to 48 00:02:21,820 --> 00:02:22,420 20. 49 00:02:22,540 --> 00:02:23,890 So odd is equal to ten. 50 00:02:24,130 --> 00:02:26,830 And the area of the circle will be Pyar Square. 51 00:02:26,830 --> 00:02:27,130 Right. 52 00:02:27,280 --> 00:02:29,500 That also is equal to three hundred and fourteen. 53 00:02:29,680 --> 00:02:35,440 Therefore, over here also it's 400 minus three hundred and fourteen which is equal to eighty six centimeters 54 00:02:35,440 --> 00:02:35,830 square. 55 00:02:36,010 --> 00:02:40,420 And you can see that the shaded region in both the cases is equal.